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HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES
Yang, Lei

2014, Doctor of Philosophy, Ohio State University, Mathematics.
In my thesis, I will study the product space of unit tangent bundles of several non-compact hyperbolic spaces, and consider the diagonal geodesic flow on this product space. We define the divergent set to be the collection of points whose forward trajectories under the diagonal geodesic flow diverge. The aim of this thesis is to calculate the Hausdorff dimension of the divergent set.

If we assume every component has finite volume, then the exact value of the Hausdorff dimension is established. If we drop the finite volume condition, but assume every component is geometrically finite, then the lower bound of the Hausdorff dimension is established unconditionally, and if we further assume that every component has the same critical exponent, then it is proved that the given lower bound is the exact value of the Hausdorff dimension.
Nimish Shah (Advisor)
Jean-Francois Lafont (Committee Member)
Vitaly Bergelson (Committee Member)
78 p.

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Yang, L. (2014). HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Yang, Lei. "HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES." Electronic Thesis or Dissertation. Ohio State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Yang, Lei "HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES." Electronic Thesis or Dissertation. Ohio State University, 2014. https://etd.ohiolink.edu/

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